越览（98）——精读复刻论文的对比分析（2）

摘要：This issue will introduce the comparative analysis of the intensively read replica paper "Emergency decision-making method based o

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“越览（98）——精读复刻论文

《基于多粒度概率语言和双参照点的

应急决策方法》对比分析（2）。”

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Today, the editor brings the

"Yue Lan(98)—intensive reading replica paper

'Emergency decision-making method based on

multi-granularity probability language

and dual reference points

'comparative analysis (2)".

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一、内容摘要（Summary of content）

本期推文将从思维导图、精读内容、知识补充三个方面介绍精读复刻论文《基于多粒度概率语言和双参照点的应急决策方法》的对比分析（2）。

This issue will introduce the comparative analysis of the intensively read replica paper "Emergency decision-making method based on multi-granularity probability language and dual reference points" in terms of mind maps, intensively read content, and knowledge supplementation.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

为了验证本文所提方法的有效性和优越性，本文将从关键风险因素的权重确定方法和可行方案的选择方法两个方面与现有的方法进行了对比分析。

In order to verify the effectiveness and superiority of the method proposed in this paper, this paper will compare and analyze it with the existing methods from two aspects: the method of determining the weights of key risk factors and the method of selecting feasible solutions.

作者在应急方案选择方法的比较分析部分将前景理论中基于单参照点的分析方法和传统的期望效用理论应用于本案例与本文方法的结果进行对比，需要指出的是，基于单参照点的方法分别考虑选取底线目标和理想目标为参照点的情形。

In the comparative analysis of emergency plan selection methods, the author applied the single reference point analysis method in prospect theory and the traditional expected utility theory to this case and compared the results with those of the method in this article. It should be pointed out that the single reference point-based method considers the situations of selecting bottom-line targets and ideal targets as reference points respectively.

上周基于单参照点中的底线目标进行了代码复刻，本周将基于单参照点中的理想目标进行了代码复刻。

Last week, the code was re-forked based on the bottom line goal in the single reference point, and this week the code will be re-forked based on the ideal goal in the single reference point.

依据调整后的代码计算出不同可行方案的最终感知价值如下图所示：

The final perceived value of different feasible solutions calculated based on the adjusted code is shown in the following figure:

可以发现基于底线目标单参照点的前景理论方法得到的可行方案排序为X2>X1>X3。与本文所得结果一致。

It can be found that the feasible solutions obtained by the prospect theory method based on the bottom line target single reference point are ranked as X2>X1>X3, which is consistent with the results obtained in this paper.

基于单参照点和双参照点的前景理论方法得到的排序结果是一致的，然而，从不同方法确定的各方案综合评价值可以看出，仅考虑底线目标时，会有更多可行方案带来的损失小于应急决策组的预期；仅考虑理想目标时，会有更多可行方案带来的损失大于应急决策组的预期；依据双参照点的分析方法同时考虑了底线目标和理想目标，更客观地体现了决策成员的主观偏好。

The ranking results obtained by the prospect theory method based on single reference point and double reference point are consistent. However, from the comprehensive evaluation values of each plan determined by different methods, it can be seen that when only the bottom line goal is considered, there will be more feasible plans that will bring losses less than the expectations of the emergency decision-making group; when only the ideal goal is considered, there will be more feasible plans that will bring losses greater than the expectations of the emergency decision-making group; the analysis method based on the double reference point considers both the bottom line goal and the ideal goal at the same time, which more objectively reflects the subjective preferences of decision-makers.

四、知识补充（Knowledge supplement）

数字标度法是一种用于对数据进行量化和标准化处理的数学方法，目的是将不同特征、不同量纲的数值数据转换为统一的标准格式，便于后续分析和比较。数字标度法广泛应用于数据科学、决策分析、工程建模等领域，尤其是在多标准决策分析、机器学习和大数据处理中有重要应用。

Digital scaling is a mathematical method used to quantify and standardize data. Its purpose is to convert numerical data of different characteristics and dimensions into a unified standard format for subsequent analysis and comparison. Digital scaling is widely used in data science, decision analysis, engineering modeling and other fields, especially in multi-criteria decision analysis, machine learning and big data processing.

以下是数字标度法的详细介绍：

1. 数字标度法的基本概念（Basic concepts of digital scaling）

数字标度法的核心思想是对不同类型、不同量纲的数据进行转换，使它们具有可比性和统一性。在实际数据分析中，原始数据通常来源于多个不同的领域，可能会包含不同的计量单位、范围和尺度。因此，必须对这些数据进行标准化或归一化处理，以便进行有效的比较、整合和分析。

The core idea of digital scaling is to convert data of different types and dimensions to make them comparable and unified. In actual data analysis, raw data usually comes from multiple different fields and may contain different units, ranges and scales. Therefore, these data must be standardized or normalized for effective comparison, integration and analysis.

数字标度法通过一系列的数学变换，将原始数据转化为一个标准范围内的数字值，确保各个数据指标在同一标准下被处理。

The digital scaling method converts the original data into digital values within a standard range through a series of mathematical transformations, ensuring that each data indicator is processed under the same standard.

2. 数字标度法的类型（Types of digital scaling）

常见的数字标度法主要包括以下几种：

Common digital scaling methods include the following:

3. 数字标度法的应用（Application of digital scaling）

(1) 数据预处理（Data preprocessing）

在机器学习和数据挖掘中，数据预处理是一个关键步骤。数字标度法可以用来对数据进行标准化或归一化，以便不同的数据特征可以在同一尺度下进行建模。尤其在使用梯度下降等优化算法时，标准化的数据能够加速收敛过程，避免因数据范围差异过大导致的优化困难。

Data preprocessing is a key step in machine learning and data mining. Digital scaling can be used to standardize or normalize data so that different data features can be modeled on the same scale. Especially when using optimization algorithms such as gradient descent, standardized data can speed up the convergence process and avoid optimization difficulties caused by large differences in data ranges.

(2) 多标准决策分析（Multi-criteria decision analysis）

在多标准决策分析中，决策问题通常涉及多个不同类型的评估标准。为了对这些标准进行综合评估，需要先对各个标准进行数字标度处理。数字标度法帮助统一标准，使得不同量纲和范围的指标可以在同一框架下进行比较和加权。

In multi-criteria decision analysis, decision problems usually involve multiple different types of evaluation criteria. In order to comprehensively evaluate these criteria, it is necessary to first perform digital scaling on each criterion. Digital scaling helps unify the criteria so that indicators of different dimensions and ranges can be compared and weighted under the same framework.

例如，在TOPSIS方法中，通过对各个指标进行标准化，使得评估对象的各项指标可以进行加权计算，最终得到一个综合评分。

For example, in the TOPSIS method, by standardizing each indicator, the indicators of the evaluation object can be weighted and calculated to obtain a comprehensive score.

(3) 风险评估和信用评分（Risk assessment and credit scoring）

在金融领域，数字标度法常用于信用评分和风险评估中。通过将客户的各种财务指标（如收入、负债、资产等）进行标准化，可以在不同的贷款申请者之间做出公正的信用评估。

In the financial sector, numerical scaling is often used in credit scoring and risk assessment. By standardizing various financial indicators of customers (such as income, liabilities, assets, etc.), a fair credit assessment can be made among different loan applicants.

(4) 图像处理和信号处理（Image processing and signal processing）

在图像处理和信号处理中，常常需要对图像的像素值进行归一化或标准化，尤其是在深度学习和图像识别中，标准化后的数据能够更好地训练模型，提高算法的稳定性和效率。

In image processing and signal processing, it is often necessary to normalize or standardize the pixel values of the image. Especially in deep learning and image recognition, the standardized data can better train the model and improve the stability and efficiency of the algorithm.

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